\section{Conclusion}

In this thesis we have shown that $\familyOf{GCSML}$ is an abstract family of matrices. It is impossible to show that this is an abstract family of languages due to the fact that $\familyOf{GCSML}$ is not closed under unrestricted morphisms, row concatenation and row closure. That is why the notion of abstract families of matrices was introduced in \cite{giftsironmoneyranisironmoney1972abstract}. 

There exists an extension of the common matrix grammars which overcomes the problem of closure under common two-dimensional morphisms. This extension coordinates the vertical derivation with tables where a table is a set of rules. A vertical derivation can only be applied if any vertical rule of this derivation is in the same table (see~\cite{sironmoney1977parallelsequential}). The languages generated by those grammars are closed under two-dimensional morphisms. 

As further work, one can show that $\familyOf{GCSML}$ is not closed under row concatenation, row closure, and general morphisms. Furthermore, one can show that $\familyOf{GCSML}$ with tables are closed under two-dimensional morphisms. 